SATHEE: Gravitation - Result Question 28

Gravitation - Result Question 28

29. Infinite number of bodies, each of mass $2 k g$ are situated on $x$ -axis at distances $1 m, 2 m, 4 m$ , $8 m, \dots .$ . respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

[2013]

(a) $- \frac{8}{3} G$

(b) $- \frac{4}{3} G$

(c) $- 4 G$

(d) - G

Show Answer

Answer:

Correct Answer: 29. (c)

Solution:

(c)

Gravitational potential $V = \frac{- G m}{r}$

$V_{0} = - \frac{G \times 2}{1} - \frac{G \times 2}{2} - \frac{G \times 2}{4} - \frac{G \times 2}{8} - \infty$

$V_{0} = - 2 G [1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots \infty]$

$V_{0} = - 2 G \times \frac{1}{(1 - \frac{1}{2})} = - 2 G \times \frac{1}{\frac{1}{2}} = - 4 G$ .

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